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We propose a sparse regression method capable of discovering the governing partial differential equation(s) of a given system by time series measurements in the spatial domain. The regression framework relies on sparsity promoting…
Extracting governing equations from dynamic data is an essential task in model selection and parameter estimation. The form of the governing equation is rarely known a priori; however, based on the sparsity-of-effect principle one may…
Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…
A new sparse semiparametric model is proposed, which incorporates the influence of two functional random variables in a scalar response in a flexible and interpretable manner. One of the functional covariates is included through a…
As power systems evolve with the increasing integration of renewable energy sources and smart grid technologies, there is a growing demand for flexible and scalable modeling approaches capable of capturing the complex dynamics of modern…
In many problems of data-driven modeling for dynamical systems, the governing equations are not known a priori and must be selected phenomenologically from a large set of candidate interactions and basis functions. In such situations, point…
The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression emerged as a…
Atomistic modelling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an…
This technical note considers the identification of nonlinear discrete-time systems with additive process noise but without measurement noise. In particular, we propose a method and its associated algorithm to identify the system nonlinear…
In this work, we propose an adaptive sparse learning algorithm that can be applied to learn the physical processes and obtain a sparse representation of the solution given a large snapshot space. Assume that there is a rich class of…
With the rapid increase of available data for complex systems, there is great interest in the extraction of physically relevant information from massive datasets. Recently, a framework called Sparse Identification of Nonlinear Dynamics…
This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…
In this work, we address the problem of identifying sparse continuous-time dynamical systems when the spacing between successive samples (the sampling period) is not constant over time. The proposed approach combines the…
Approximating field variables and data vectors from sparse samples is a key challenge in computational science. Widely used methods such as gappy proper orthogonal decomposition and empirical interpolation rely on linear approximation…
This manuscript goes through the fundamental connections between statistical mechanics and estimation theory by focusing on the particular problem of compressive sensing. We first show that the asymptotic analysis of a sparse recovery…
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…
Trajectory optimization of a controlled dynamical system is an essential part of autonomy, however many trajectory optimization techniques are limited by the fidelity of the underlying parametric model. In the field of robotics, a lack of…
Experimental data is often affected by uncontrolled variables that make analysis and interpretation difficult. For spatiotemporal systems, this problem is further exacerbated by their intricate dynamics. Modern machine learning methods are…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
The dynamics of mechanical systems such as turbomachinery with multiple blades are often modeled by arrays of periodically driven coupled nonlinear oscillators. It is known that such systems may have multiple stable vibrational modes, and…